Spatial-temporal data arises in many applications, for example, environment sciences and disease mapping. This dissertation focuses on Gaussian spatial-temporal data. To make statistical inference for Gaussian spatial-temporal data, we developed a special class of spatial-temporal Gaussian state-space models in which the state vectors are constructed following spatial-temporal Gaussian autoregressions that...
Image classification is a difficult problem, often requiring large training sets to get satisfactory results. However this is a task that humans perform very well, and incorporating user feedback into these learning algorithms could help reduce the dependency on large amounts of labeled training data. This process has already been...
This dissertation examines properties and representations of several isotropic Gaussian random fields in the unit ball in d-dimensional Euclidean space. First we consider Lévy's Brownian motion. We use an integral representation for the covariance function to find a new expansion for Lévy's Brownian motion as an infinite linear combination of...
Supervised learning is concerned with discovering the relationship between example sets of features and their corresponding classes. The traditional supervised learning formulation assumes that all examples are independent from one another. The order of the examples contains no information. Nonetheless, many problems have a sequential nature. Classifiers for these problems...
This dissertation presents some results from various areas of probability theory, the unifying theme being the use of functional analytic intuition and techniques. We first give a result regarding the existence of certain stochastic integral representations for Banach space valued Gaussian random variables. Next we give a spectral geometric construction...
Sequential supervised learning problems arise in many real applications. This dissertation focuses on two important research directions in sequential supervised learning: efficient training and feature induction.
In the direction of efficient training, we study the training of conditional random fields (CRFs), which provide a flexible and powerful model for sequential...
Modern digital still cameras are equipped with just a single CCD for color image acquisition. Since only one spectral band can be recorded in each pixel, a mosaic of red, green and blue color filters is placed in front of the chip. The process of subsequently calculating a full color...
Random fields are frequently used in computational simulations of real-life processes. In particular, in this work they are used in modeling of flow and transport in porous media. Porous media as they arise in geological formations are intrinsically deterministic but there is significant uncertainty involved in determination of their properties...
The major limiting factor of DRAM access time is the low transconductance of the
MOSFET's which have only limited current drive capability. The bipolar junction
transistor(BJT) has a collector current amplification factor, β, times base current and is
limited mostly by the willingness to supply this base current. This collector...